We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using cent...We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using center manifold theorem and normal form.At last some simulations are given to support our results.展开更多
In this article,a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically.The Monod-Haldane functional response is considered for non...In this article,a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically.The Monod-Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate.The model analysis shows that the model has two equilibria which are named as disease-free equilibrium(DFE)and endemic equilibrium(EE).The stability analysis has been performed for the local and global behavior of the DFE and EE.With the help of the basic reproduction number(R_(0)),we investigate that DFE is locally asymptotically stable when R_(0)<1 and unstable when R_(0)>1.The local stability of DFE at R_(0)=1 has been analyzed,and it is obtained that DFE exhibits a forward transcritical bifurcation.Further,we identify conditions for the existence of EE and show the local stability of EE under certain conditions.Moreover,the global stability behavior of DFE and EE has been investigated.Lastly,numerical simulations have been done in the support of our theoretical findings.展开更多
文摘We analysis Hopf bifurcation in a Monod-Haldane predator-prey model with three delays in this paper.Fixingτ1 andτ2 and takingτ3 as parameter,the direction and stability of Hopf bifurcation are studied by using center manifold theorem and normal form.At last some simulations are given to support our results.
文摘In this article,a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically.The Monod-Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate.The model analysis shows that the model has two equilibria which are named as disease-free equilibrium(DFE)and endemic equilibrium(EE).The stability analysis has been performed for the local and global behavior of the DFE and EE.With the help of the basic reproduction number(R_(0)),we investigate that DFE is locally asymptotically stable when R_(0)<1 and unstable when R_(0)>1.The local stability of DFE at R_(0)=1 has been analyzed,and it is obtained that DFE exhibits a forward transcritical bifurcation.Further,we identify conditions for the existence of EE and show the local stability of EE under certain conditions.Moreover,the global stability behavior of DFE and EE has been investigated.Lastly,numerical simulations have been done in the support of our theoretical findings.
